Receptors diffusing over the surface of a cell allow it to sense its environment and respond to it. Often the aggregation of these receptors is crucial to the triggering of cellular responses. We focus on three types of cell surface receptor aggregation, induced by three types of ligands (antigens, antibodies and lymphokines) that play important roles in the immune response. 1. Antigens aggregate cell surface immunoglobulin (sIg) and in the process initiate responses in B lymphocytes, basophils and mast cells. 2. Anti-sIg solution antibodies (IgG) span sIg and Fcgamma receptors and on B lymphocytes these co-crosslinks inhibit signals generated by aggregated sIg. 3. Interleukin 2 (IL-2), induces the aggregation of IL-2 receptors on activated T cells generating signals that lead to the control of T cell growth and IL-2 secretion. Our aim is to understand to develop mathematical models that can predict the time course of such aggregate formation, and to relate this aggregation to specific cellular responses. The role of the mathematical models is to help devise rigorous test of ideas about the system, aid in analyzing experiments, determine parameter values, and suggest new experiments. We use rat basophilic leukemia (RBL) cells sensitized with monoclonal anti- hapten IgE as a model system for studying general features of receptor aggregation as well as specific effects of sIg aggregation and sIg-FcgammaR co-crosslinking. The formation of IgE aggregates on RBL cells triggers numerous cellular responses, but not all aggregates trigger all responses. To determine what properties are required of an IgE aggregate to make it an effective initiator of a particular response we will fully characterize the binding properties of haptens of different lengths, flexibilities and valence so that we can predict how the distribution of hapten-IgE with the responses of the RBL cell surfaces. We then will compare these predictions with the responses of the RBL cell (Ca2+ fluxes, degranulation, cytoskeletal interactions, IgE internalization), to relate surface aggregates to cellular responses. We also will use the RBL system to study the initial events (and how to block them) that occur when a large antigen or virion attaches to a cell surface. In building a mathematical model of the interaction of IL-2 with its surface receptors, we focus on experiments using T cell clones expressing different concentrations of light and heavy chain receptors. The studies in this project are health related, bearing on allergic reactions and their treatment, normal and abnormal T cell growth, and other aspects of the immune response.